Logic -> Proof -> Rest, 2018 The College of Wooster

#### Logic -> Proof -> Rest, Maxwell Taylor

*Senior Independent Study Theses*

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

Model-Completions And Model-Companions, 2017 Wesleyan University

#### Model-Completions And Model-Companions, Mostafa Mirabi

*Mostafa Mirabi*

Neutrosophic Hough Transform, 2017 University of New Mexico

#### Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur

*Mathematics and Statistics Faculty and Staff Publications*

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its ...

Graph Structures In Bipolar Neutrosophic Environment, 2017 University of New Mexico

#### Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara

*Mathematics and Statistics Faculty and Staff Publications*

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

Neutrosophic Commutative N-Ideals In Bck-Algebras, 2017 University of New Mexico

#### Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun

*Mathematics and Statistics Faculty and Staff Publications*

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.

Neutrosophic N -Structures And Their Applications In Semigroups, 2017 University of New Mexico

#### Neutrosophic N -Structures And Their Applications In Semigroups, Florentin Smarandache, Madad Khan, Saima Anis, Young Bae Jun

*Mathematics and Statistics Faculty and Staff Publications*

The notion of neutrosophic N -structure is introduced, and applied it to semigroup. The notions of neutrosophic N -subsemigroup, neutrosophic N -product and ε-neutrosophic N -subsemigroup are introduced, and several properties are investigated. Conditions for neutrosophic N -structure to be neutrosophic N -subsemigroup are provided. Using neutrosophic N -product, characterization of neutrosophic N -subsemigroup is discussed. Relations between neutrosophic N -subsemigroup and εneutrosophic N -subsemigroup are discussed. We show that the homomorphic preimage of neutrosophic N -subsemigroup is a neutrosophic N - subsemigroup, and the onto homomorphic image of neutrosophic N - subsemigroup is a neutrosophic N -subsemigroup.

Neutrosophic N -Structures Applied To Bck/Bci-Algebras, 2017 University of New Mexico

#### Neutrosophic N -Structures Applied To Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Hashem Bordbar

*Mathematics and Statistics Faculty and Staff Publications*

Neutrosophic N -structures with applications in BCK/BC I-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BC I-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided.

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe [Presentation], 2017 Portland State University

#### Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe [Presentation], Martin Zwick, Joshua Hughes

*Systems Science Faculty Publications and Presentations*

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is ...

Ideas & Graphs, 2017 Portland State University

#### Ideas & Graphs, Martin Zwick

*Systems Science Faculty Publications and Presentations*

A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure.

This paper considers graphs (but not hypergraphs) consisting of four nodes, and suggests meanings that can be associated with several different directed and undirected graphs.

Drawing on Bennett's "systematics," specifically on the Tetrad that systematics offers as a model of 'activity,' the analysis here shows that the Tetrad is versatile model of problem-solving, regulation and control, and other processes.

Interstructure Lattices And Types Of Peano Arithmetic, 2017 The Graduate Center, City University of New York

#### Interstructure Lattices And Types Of Peano Arithmetic, Athar Abdul-Quader

*Dissertations, Theses, and Capstone Projects*

The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA.

In Chapter 2, we study a problem that had its origin in Simpson, who used arithmetic forcing to show that every countable model of PA has an expansion to PA^{∗} that is pointwise definable. Enayat later showed that there are 2^{ℵ0} models with the ...

Ns-K-Nn: Neutrosophic Set-Based K-Nearest Neighbors Classifier, 2017 University of New Mexico

#### Ns-K-Nn: Neutrosophic Set-Based K-Nearest Neighbors Classifier, Florentin Smarandache, Yaman Akbulut, Abdulkadir Sengur, Yanhui Guo

*Mathematics and Statistics Faculty and Staff Publications*

k-nearest neighbors (k-NN), which is known to be a simple and efficient approach, is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set. The k-nearest neighbors are determined based on some distance functions. Although k-NN produces successful results, there have been some extensions for improving its precision. The neutrosophic set (NS) defines three memberships namely T, I and F. T, I, and F shows the truth membership degree, the false membership degree, and the indeterminacy membership degree, respectively. In this paper, the NS ...

The Feferman-Vaught Theorem, 2017 Wesleyan University

#### The Feferman-Vaught Theorem, Mostafa Mirabi

*Mostafa Mirabi*

Complex Neutrosophic Soft Set, 2017 University of New Mexico

#### Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

Complex Neutrosophic Graphs Of Type 1, 2017 University of New Mexico

#### Complex Neutrosophic Graphs Of Type 1, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, we introduced a new neutrosophic graphs called complex neutrosophic graphs of type1 (CNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of CNG1 is an extension of generalized fuzzy graphs of type 1 (GFG1) and generalized single valued neutrosophic graphs of type 1 (GSVNG1).

Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, 2017 University of New Mexico

#### Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

*Mathematics and Statistics Faculty and Staff Publications*

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach.

Joint Laver Diamonds And Grounded Forcing Axioms, 2017 The Graduate Center, City University of New York

#### Joint Laver Diamonds And Grounded Forcing Axioms, Miha Habič

*Dissertations, Theses, and Capstone Projects*

In chapter 1 a notion of independence for diamonds and Laver diamonds is investigated. A sequence of Laver diamonds for κ is *joint* if for any sequence of targets there is a single elementary embedding *j* with critical point κ such that each Laver diamond guesses its respective target via *j*. In the case of measurable cardinals (with similar results holding for (partially) supercompact cardinals) I show that a single Laver diamond for κ yields a joint sequence of length κ, and I give strict separation results for all larger lengths of joint sequences. Even though the principles get strictly ...

Choice Of Choice: Paradoxical Results Surrounding Of The Axiom Of Choice, 2017 Union College - Schenectady, NY

#### Choice Of Choice: Paradoxical Results Surrounding Of The Axiom Of Choice, Connor Hurley

*Honors Theses*

When people think of mathematics they think "right or wrong," "empirically correct" or "empirically incorrect." Formalized logically valid arguments are one important step to achieving this definitive answer; however, what about the underlying assumptions to the argument? In the early 20th century, mathematicians set out to formalize these assumptions, which in mathematics are known as axioms. The most common of these axiomatic systems was the Zermelo-Fraenkel axioms. The standard axioms in this system were accepted by mathematicians as obvious, and deemed by some to be sufficiently powerful to prove all the intuitive theorems already known to mathematicians. However, this system ...

Neutrosophy, A Sentiment Analysis Model, 2017 University of New Mexico

#### Neutrosophy, A Sentiment Analysis Model, Florentin Smarandache, Mirela Teodorescu, Daniela Gifu

*Mathematics and Statistics Faculty and Staff Publications*

This paper describes the importance of Neutrosophy Theory in order to find a method that could solve the uncertainties arising on discursive analysis. The aim of this pilot study is to find a procedure to diminish the uncertainties from public discourse induced, especially, by humans (politicians, journalists, etc.). We consider that Neutrosophy Theory is a sentiment analysis specific case regarding processing of the three states: positive, negative, and neutral. The study is intended to identify a method to answer to uncertainties solving in order to support politician's staff, NLP specialists, artificial intelligence researchers and generally the electors.

On Tarski's Axiomatic Foundations Of The Calculus Of Relations, 2017 Hungarian Academy of Sciences

#### On Tarski's Axiomatic Foundations Of The Calculus Of Relations, Hajnal Andréka, Steven Givant, Peter Jipsen, István Németi

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown ...

Mcdm Method For N-Wise Criteria Comparisons And Inconsistent Problems, 2017 University of New Mexico

#### Mcdm Method For N-Wise Criteria Comparisons And Inconsistent Problems, Florentin Smarandache, Azeddine Elhassouny

*Mathematics and Statistics Faculty and Staff Publications*

The purpose of this paper is to present an e[xtension and alternative of the hybrid method based on Saaty’s Analytical Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution method (AHP-TOPSIS), that based on the AHP and its use of pairwise comparisons, to a new method called α -D MCDM-TOPSIS( α -Discounting Method for multicriteria decision making-TOPSIS). The new method overcomes limits of AHP which work only for pairwise comparisons of criteria to any-wise (n-wise) comparisons, with crisp coefficients or with interval-valued coefficients. α-D MCDM-TOPSIS is verified by some examples to demonstrate how it allows ...